Many studies have provided evidence for the existence of universal constraints on color categorization or naming in various languages, but the biological basis of these constraints is unknown. A recent study of the pattern of color categorization across numerous languages has suggested that these patterns tend to avoid straddling a region in color space at or near the border between the English composite categories of "warm" and "cool". This fault line in color space represents a fundamental constraint on color naming. Here we report that the two-way categorization along the fault line is correlated with the sign of the L- versus M-cone contrast of a stimulus color. Moreover, we found that the sign of the L-M cone contrast also accounted for the two-way clustering of the spatially distributed neural responses in small regions of the macaque primary visual cortex, visualized with optical imaging. These small regions correspond to the hue maps, where our previous study found a spatially organized representation of stimulus hue. Altogether, these results establish a direct link between a universal constraint on color naming and the cone-specific information that is represented in the primate early visual system.